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  • 51M20  (1)
  • convolution.  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    New Combinations of Convex Sets (1999)
    Springer
    Geometriae dedicata 78 (1999), S. 1-19 
    Details
    ISSN: 1572-9168
    Keywords: convex set ; fibre combination ; polarity ; convex function ; convolution.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The family of convex sets in a (finite dimensional) real vector space admits several unary and binary operations – dilatation, intersection, convex hull, vector sum – which preserve convexity. These generalize to convex functions, where there are in fact further operations of this kind. Some of the latter may be regarded as combinations of two such operations, acting on complementary subspaces. In this paper, a general theory of such mixed operations is introduced, and some of its consequences developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005019802841
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Realizations of regular apeirotopes (1994)
    Springer
    Aequationes mathematicae 47 (1994), S. 223-239 
    Details
    ISSN: 1420-8903
    Keywords: 51M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In an earlier paper, a theory of realizations of (finite) regular polytopes in euclidean spaces was developed. Here, the analogous problem of realizing regular apeirotopes (infinite polytopes) is investigated. While no complete theory is expounded, several basic results are established. Among these is the curious fact that, if a regular apeirotope has a discrete realization, then it has one with no translations in its symmetry group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01832961
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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